Isothermal magnetic relaxation measurements are widely used to probe energy barriers in systems of magnetic nanoparticles. Here we show that the result of such an experiment can differ greatly for aligned and randomly oriented nanoparticles. For randomly oriented cobalt-doped magnetite nanoparticles we observe a prominent low-energy tail in the energy barrier distribution that is greatly attenuated when the particles are magnetically aligned. Monte Carlo simulations show that this behaviour arises for nanoparticles with both cubic and uniaxial magnetic anisotropy energy terms even though for cubic or uniaxial anisotropy alone the energy barrier distribution is independent of nanoparticle orientation.